Rewrite as a simplified fraction. ${2.2\overline{7} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 227.7777...\\ 10x &= 22.7777...\end{align*}}$ Subtracting the two equations, we have: ${90x = 205}$ ${x = \dfrac{205}{90}} $ ${x = \dfrac{41}{18}} \text{or} {2 \dfrac{5}{18}}$